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TECHNICAL PAPERS

# Robustness Limitations in Self-Sensing Magnetic Bearings

[+] Author and Article Information
Eric H. Maslen

Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA 22904-4746ehm7s@virginia.edu

Dominick T. Montie, Tetsuya Iwasaki

Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA 22904-4746

A recently proposed ISO standard (14839-3) for AMB systems recommends a threshold sensitivity of 3.0 for acceptance of commercial systems, based on consensus of industry experts. Of course, this number may be revised up or down as more experience with application of the standard becomes available.

The estimation is performed on the time scale of the switching wave form, which can be much shorter than the typical time scales of the electrodynamic system.

These numerical values for $Φ0$ and $η$ do not actually appear in Ref. 15. For purposes of the present discussion, these values were computed using the nondimensionalization discussed in 2 and the physical parameters presented in Ref. 15.

J. Dyn. Sys., Meas., Control 128(2), 197-203 (Apr 22, 2005) (7 pages) doi:10.1115/1.2192820 History: Received November 25, 2003; Revised April 22, 2005

## Abstract

Self-sensing magnetic bearings use measurements of voltage and current in electromagnets to estimate the position of a magnetically levitated object. By estimating position in this manner, explicit proximity sensors are eliminated, along with significant cost, weight, and hardware complexity. Motivated by early and discouraging experimental studies, several theoretical papers have concluded an inherent difficulty in employing self-sensing. In light of later experimental work that appears to avoid this difficulty, we argue that these conclusions may be attributed to an over-simplification in the model from which this apparent difficulty is inferred. Specifically, if a linear time-invariant (LTI) model is derived from the underlying nonlinear model by linearizing the system at a fixed equilibrium point, analysis of this LTI model leads to the incorrect conclusion that self-sensing cannot be robust. The present work establishes that, if essential features of the nonlinearity are retained by linearization along a periodic trajectory, analysis of the resulting linear periodic model predicts more acceptable levels of robustness.

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## Figures

Figure 1

Active magnetic bearing

Figure 2

Switching amplifier and resulting switching current ripple

Figure 3

Definitions of sensitivity functions

Figure 4

Effect of σ on sensitivity norm bound

Figure 5

Effect of γ and ω on the input sensitivity function norm

Figure 6

Effect of γ and ω on the output sensitivity function norm

Figure 7

Weighting filter to distinguish between LTI and LP uncertainty operators

Figure 8

Effect of γ and ω on the output sensitivity function norm with filter B(s) inserted

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